Developing more robust control theory models 

Jonathan Partington is currently professor at the University of Leeds, UK. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Centre for Mathematical Sciences, Lund University, Sweden. 

Systems described by infinite-dimensional linear equations systems have attracted increasing interest in the last two decades. The study of such systems is a branch of the much broader area of control theory, which originated in the study of engineering problems. Similar mathematical models have been developed for a wide range of dynamical systems and have been successfully applied in aeronautics, electronics, biology, material sciences, and many other fields. 

A fundamental research question is the robustness of the system development with time, otherwise known as the well-posedness problem. Well-posedness indicates how sensitive solutions are to different initial conditions. Will a small change in initial values cause only a small change in the outcomes? Or, on the contrary, will the final signals deviate significantly due to small changes in the beginning? 

 
Researchers involved in the proposed project have solved certain special cases of the problem. They have successfully combined methods in linear systems with those of other fields of mathematics: harmonic analysis and complex analysis. The goal of the project is to extend this research to other cases and to a more general setting. Jonathan Partington’s interests in fundamental research and its applications overlap those of several researchers in Lund and in Göteborg. In particular, he has a long-term collaboration with Professor Sandra Pott on developments in mathematical control theory.

Photo: University of Leeds